Solution to a differential equation, Mathematics

Assignment Help:

A solution to a differential equation at an interval α < t < b is any function y (t) that satisfies the differential equation in question on the interval α < t < b.  It is significant to note that solutions are frequently accompanied through intervals and these intervals can impart several of significant information regarding the solution.  Consider the subsequent illustration.

Illustration 1:  Show that y(x) = x-3/2 is a solution to 4x2 y′′ + 12xy′ + 3 y = 0 for x > 0.

Solution: We'll require the first and second derivative to do this.

y'(x) = (-3/2) x-5/2                     y''(x) = (15/4) x-7/2

Plug these in addition to the function in the differential equation.

4x2 ((15/4) x-7/2) + 12x((-3/2) x-5/2) + 3(x-3/2) = 0


Related Discussions:- Solution to a differential equation

Write the value of sin10+sin20+sin30+....+sin360., sin10+sin20+sin30+....+s...

sin10+sin20+sin30+....+sin360=0 sin10+sin20+sin30+sin40+...sin180+sin(360-170)+......+sin(360-40)+sin(360-30)+sin(360-20)+sin360-10)+sin360 sin360-x=-sinx hence all terms cancel

Define a cyclic group, Question 1: (a) Show that, for all sets A...

Question 1: (a) Show that, for all sets A, B and C, (i) (A ∩ B) c = A c ∩B c . (ii) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C). (iii) A - (B ∪ C) = (A - B) ∩ (A - C).

Learning to count in maths, Here we learn: 1) Discussed what counting me...

Here we learn: 1) Discussed what counting means, and stressed that it is not the ability to recite number names. 2) Talked about the need for a child to understand several pr

Marketing research, Discuss the role research would play during your decisi...

Discuss the role research would play during your decision making

How to join as maths expert, Sir, With due respect,I, beg to state that I ...

Sir, With due respect,I, beg to state that I want to join as a maths expert and earn some money. I would be grateful to you if you guide me in this regard.

Determine multiplications required to obtain the determinant, Don't count t...

Don't count the number of divisions. Do not use asymptotic notation, instead provide exact answers. (i) What is the maximum number of multiplications required to solve a system

Z-value, A study was conducted to determine the proportion of people who dr...

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 317317 people over the age of? 55, 7777 dream in black and? whi

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd